The Forgiver, The Ever-Forgiving, The Most-Forgiving.
Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ is Al-Ghaffar (in Arabic: ٱلْغَفَّارُ), He sees our sins and disobedience, yet He still forgives and accepts the repentance of the sincere. He shows never-ending compassion and forgiveness, no matter how big or small the sin. He is the most forgiving and loves to forgive.
From the root ghayn-fa-ra (غ ف ر), which has the following classical Arabic connotations: to cover, veil, conceal, hide to pardon, to forgive, to set aright, to cover a thing, to protect it from dirt.
The names Al-Ghaffar, Al-Ghaffur, and Al-Ghafir all refer to Allah's attribute of being forgiving. Together they have been mentioned a total of 97 times in the Qur'an. Of those 97 instances, the Qur'an mentions Al-Ghaffur 91 times, Al-Ghaffar 5 times, and Al-Ghafir just once.
Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ loves to forgive:
These names refer to Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ nature of being forgiving. He wants to forgive those who seek istighfar (forgiveness). Anas (May Allah be pleased with him) reported: Messenger of Allah ﷺ said, "Allah, the Exalted, has said: 'O son of adam, I forgive you as long as you pray to Me and hope for My forgiveness, whatever sins you have committed. O son of 'Adam, I do not care if your sins reach the height of the heaven, then you ask for my forgiveness, I would forgive you. O son of 'Adam, if you come to Me with an earth load of sins, and meet Me associating nothing to Me, I would match it with an earthload of forgiveness."' 
From this hadith, we learn that it's never too late for someone who seeks the forgiveness of their Lord, even if their sins "reach the height of the heaven." Do not ever feel you are overburdening, asking for too much, or it's too late. This would be insulting to Allah's mercy, who is Al-Ghaffar, The Oft-Forgiving, the one who forgives perpetually. A person who has sinned should not despair of Allah's mercy. We are told in the following verse the one who sins has only wronged themselves when they disobey Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ. They have not wronged Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ but cheated themselves out of some goodness. Like a person who cheats on a test. They may get a good grade in the class but will miss the benefit of having that knowledge and will pay the price in the real world.
Qul yaa’ibaadiyal lazeena asrafoo ‘alaaa anfusihim laa taqnatoo mirrahmatil laah; innal laaha yaghfiruz zunooba jamee’aa; innahoo Huwal Ghafoorur Raheem
"Say, 'O My servants who have transgressed against themselves [by sinning], do not despair of the mercy of Allah. Indeed, Allah forgives all sins. Indeed, it is He who is the Forgiving, the Merciful.'" — (Qur'an 39:53)
Faqultus taghfiroo Rabakum innahoo kaana Ghaffaaraa
"And said, ‘Ask forgiveness of your Lord. Indeed, He is ever a Perpetual Forgiver." — (Qur'an 71:10)
Even what's regarded as the unpardonable sin shirk (i.e., associating partners with Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ) can be forgiven. In the Qur'an, it says, "Indeed, Allah does not forgive association with Him, but He forgives what is less than that for whom He wills. And he who associates others with Allah has certainly fabricated a tremendous sin" (Qur'an 4:48) and in another verse, "Indeed, Allah does not forgive association with Him, but He forgives what is less than that for whom He wills. And he who associates others with Allah has certainly gone far astray." (Qur'an 4:116) But as other commentators have pointed out in Surah Az-Zumar, "Indeed, Allah forgives all sins." All the sahabah before the Prophet's time were considered mushrikeen, but they changed, they sought forgiveness, and Allah forgave them. The Qur'an only speaks of the person not being forgiven if they died having committed shirk (e.g., Prophet Ibrahim AS father who died a pagan) and chose to reject or deny Islam.
The remaining Quranic verses that include the name Al-Ghaffar.
Wa innee la Ghaffaarul liman taaba wa aamana wa ‘amila saalihan summah tadaa
"But indeed, I am the Perpetual Forgiver of whoever repents and believes and does righteousness and then continues in guidance." — (Qur'an 20:82)
Rabbus samaawaati wal ardi wa maa bainahumal Azeezul Ghaffaar
"Lord of the heavens and the earth and whatever is between them, the Exalted in Might, the Perpetual Forgiver." — (Qur'an 38:66)
Khalaqas samaawaati wal arda bilhaqq; yukawwirul laila ‘alan nahaari wa yukawwirun nahaara ‘alaal laili wa sakhkharash shamsa walqamara kulluny yajree li ajalim musammaa; alaa Huwal ‘Azeezul Ghaffaar
"He created the heavens and earth in truth. He wraps the night over the day and wraps the day over the night and has subjected the sun and the moon, each running [its course] for a specified term. Unquestionably, He is the Exalted in Might, the Perpetual Forgiver." — (Qur'an 39:5)
Tad'oonanee li-akfura billaahi wa ushrika bihee maa laisa lee bihee ilmunw wa ana ad’ookum ilal'Azeezil Ghaffaar
"You invite me to disbelieve in Allah and associate with Him that of which I have no knowledge, and I invite you to the Exalted in Might, the Perpetual Forgiver." — (Qur'an 40:42)
|Name Pairings||# of Times|
|Al-Haleem (The Clement One)||4|
|Al-Afuww (The Effacer of Sins)||4|
|Al-Aziz (The Eminent)||2|
*These are some of the pairings with Al-Ghaffar & Al-Ghafoor.
Abu Huraira reported Allah's Apostle (ﷺ) as saying: The servant (who conceals) the faults of others in this world, Allah would conceal his faults on the Day of Resurrection. The lesson behind this is not to conceal unlawful acts from authorities per se but rather to serve as a reminder to avoid searching for the ugliness in people.
Some people actively look, and when they find it, they are delighted. They have an inherent distrust in people, and so when their suspicion is confirmed - they are pleased. Others may find pleasure in seeing the fault in others as a way to avoid dealing with their deficiencies.
What is better for the believer is to look for the good, just as Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ wants to forgive His servants. He wants those who make mistakes to rise above them, i.e., to seek His forgiveness and to be better because of it. We should give people the same opportunity. It does take being vulnerable to some extent, but that is not a weakness. Lead with love, trust, and compassion. Only once your kindness is taken advantage of should you review your terms of interaction with that particular individual. Be oft-forgiving and avoid growing bitter towards humanity at large.